Pluripotential theory on quaternionic manifolds

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Abstract

On any quaternionic manifold of dimension greater than 4 a class of plurisubharmonic functions (or, rather, sections of an appropriate line bundle) is introduced. Then a Monge-Ampère operator is defined. It is shown that it satisfies a version of the theorems of A. D. Alexandrov and Chern-Levine-Nirenberg. For more special classes of manifolds analogous results were previously obtained in Alesker (2003). [1] for the flat quaternionic space Hn and in Alesker and Verbitsky (2006). [5] for hypercomplex manifolds. One of the new technical aspects of the present paper is the systematic use of the Baston differential operators, for which we also prove a new multiplicativity property.

Original languageEnglish
Pages (from-to)1189-1206
Number of pages18
JournalJournal of Geometry and Physics
Volume62
Issue number5
DOIs
StatePublished - May 2012

Keywords

  • Monge-Ampere operator
  • Plurisubharmonic functions
  • Quaternionic manifolds

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